Emergent gravity from Eguchi-Kawai reduction

TL;DR

This paper explores how the Eguchi-Kawai reduction mechanism underpins features of holographic theories with gravity duals, illustrating its role in the emergence of gravity and the transition from higher-spin theories to string theories.

Contribution

It proposes that the Eguchi-Kawai mechanism explains key features of holographic dualities and demonstrates how its failure and restoration relate to higher-spin and string theory transitions.

Findings

Eguchi-Kawai mechanism controls holographic features

Higher-spin holography is linked to Eguchi-Kawai failure

Restoration of the mechanism relates to string theory emergence

Abstract

Holographic theories with a local gravitational dual have a number of striking features. Here I argue that many of these features are controlled by the Eguchi-Kawai mechanism, which is proposed to be a hallmark of such holographic theories. Higher-spin holographic duality is presented as a failure of the Eguchi-Kawai mechanism, and its restoration illustrates the deformation of higher-spin theory into a proper string theory with a local gravitational limit. AdS/CFT is used to provide a calculable extension of the Eguchi-Kawai mechanism to field theories on curved manifolds and thereby introduce "topological volume independence." Finally, I discuss implications for a general understanding of the extensivity of the Bekenstein-Hawking-Wald entropy.